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On Serre dimension of monoid algebras and Segre extensions
Journal
Journal of Pure and Applied Algebra
ISSN
00224049
Date Issued
2022-09-01
Author(s)
Keshari, Manoj K.
Mathew, Maria A.
Abstract
Let R be a commutative noetherian ring of dimension d and M be a commutative, cancellative, torsion-free monoid of rank r. Then S-dim(R[M])≤max{1,dim(R[M])−1}. Further, we define a class of monoids {Mn}n≥1 such that if M∈Mn is seminormal, then S-dim(R[M])≤dim(R[M])−n=d+r−n, where 1≤n≤r. As an application, we prove that for the Segre extension Smn(R) over R, S-[Formula presented].
Volume
226
Publication link
Subjects